The .aamt Substrate: Memory-Mapped Hexadeca-Tree Storage and Zero-Copy Geometric Routing (the Micro-VM Layer)

The AAMT series has produced three runnable memory systems: topologically protected trit anchors (EXP-01), voxel-steered output eviction over a TERA/HNSW index (WP-21), and Odu coverage maps for loop escape (WP-22). Each currently persists through a different ad-hoc path — TSV, JSON, Python dictionaries, and an HNSW sidecar — so every session pays a full parse-and-rebuild cost, and no two surfaces of the platform (desktop Python, browser visualizer, Unity) can open the same artifact. This paper specifies the .aamt substrate: a single memory-mapped binary format holding a hexadeca-tree spatial index over the 4D TERA cube, with 64-byte cache-line nodes, popcount-indexed sparse children, a zero-copy payload arena, and a deterministic sidecar journal that makes every query bit-exactly replayable. The load-bearing structural result is the orthant correspondence: a binary split of 4D TERA space yields exactly 24 = 16 children per node — the 16 Meji — and two tree levels yield exactly 16 × 16 = 256 cells — the 256 Odu. The Meji/Odu lattice is therefore not a naming convention layered on the index; it is the unique natural spatial index of TERA space, and a query's routing path is literally an Odu word. We position the substrate honestly: it is the geometric memory layer that runs beside a conventional LLM runtime (the architecture WP-21 already established), not a replacement for transformer weights, and its routing cost is O(depth) — bounded and scan-free — not O(1). The substrate's first production integration (Section 9, memory_index_bridge.py) then falsified its own most obvious application: reconstructing a bulk id/label table through the substrate loses to json.load by an order of magnitude, because per-record ctypes marshalling overhead dominates the native tree walk's advantage. What shipped instead — labels stay in JSON; the substrate serves a new O(depth) coarse-routing command alongside HNSW's fine discrimination — is the correction, and it is the more interesting result: the right division of labor was not the one first assumed, and measurement found it in under an hour rather than in production. Section 10 adds a redundancy scheme built from a single exact geometric operation — a true Householder reflection of the TERA cube's T axis, distinguished from the antipodal map (which, in this even dimension, is orientation-preserving and so not actually a mirror) — giving every record a physically separate redundant copy and a gate, verifyChirality, that catches “bad reflections” by re-deriving the relationship rather than trusting stored state; verified against real, injected byte-level corruption, not simulated failure. Revision 2 adds §13.3: a real second CRDT writer in a browser tab (aamt-crdt.js, a JS port of aamt_crdt.py exact enough to interoperate — same Hybrid Logical Clock, same (hlc, data, tera) tiebreak, same JSON interchange format). Verified two ways: aamt-crdt.js's own 500-trial property tests independently reprove the three join-semilattice laws on the JS side, and a genuine two-process, two-language integration — a real browser tab wrote three records with real HLC timestamps and exported them; a real, separate Python process imported that JSON, merged it with independent writes including a deliberate id collision, and packed the converged result to a real .aamt file with the correct winner. A real cross-language bug was found and fixed by this testing, not assumed: a 63-bit replica_id exceeds JavaScript's 253 safe-integer range, so the JS side must serialize it as a JSON string, which Python's to_json now always emits. Still not “live” in the WP-25 integration sense — no shipped consumer generates real cross-device writes yet — but the excuse “no second writer exists to test against” is gone.